More likely voters still trust Obama to do a better job than his Republican challenger in handling the Medicare and Medicaid programs, lowering healthcare costs and determining the future of the healthcare law he signed in 2010.

But Romney has cut the president’s lead in half on most issues and nearly eliminated it entirely on Medicare, the Kaiser survey found, compared with a similar poll taken in September.

On the question of determining the future Medicare, 46% of likely voters said they trust Obama to do a better job, compared with 41% who trust Romney. In September, the president held a 52%-to-36% advantage.

Obama leads Romney, 46% to 39%, on the question of whom voters trust to determine the future of the Medicaid program for the poor. That’s down from an edge of 53% to 35% in September.

The president’s lead on whom voters trust to lower healthcare costs “for people like you” is now also 46% to 39%, down from 51% to 35%.

And on the question of who can be trusted to determine the future of the Affordable Care Act, which Romney has pledged to repeal, Obama holds a 48%-to-40% advantage, compared with 53% to 36% in September.

The only healthcare question where Obama continues to hold a commanding advantage is on whom voters trust to do a better job of “making decisions about women’s reproductive health choices and services.” He is trusted by 51%, compared with 33% who trust Romney. In September, the president held a 52%-to-32% advantage.

More broadly, voters continue to be skeptical of Romney’s plan to replace the existing Medicare program with a new system that gives seniors entering the program after 2022 a set amount of money to buy either a private insurance plan or the government plan. Just 31% of likely voters support that idea, compared with 61% who say they want to preserve the current system.

Seniors are even more opposed to such a plan, with 72% saying they want to keep the current system, and 18% saying they support a change.

But older voters are less likely to trust Obama than Romney to determine the future of the Medicare program. Among likely voters 65 and older, Romney leads the president on Medicare, 48% to 43%. The former Massachusetts governor has an even bigger lead among those 55 to 64, with 53% saying they trust Romney more on Medicare and just 40% saying they trust Obama.

The survey was conducted Oct. 18-23 among a nationally representative random telephone sample of 1,215 adults ages 18 and older living in the United States.